You are considering investing $1000 in a complete portfolio. The complete portfolio is composed of Treasury notes that pay 5% and a risky portfolio, P, constructed with two risky securities X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. The dollar values of your positions in X, Y, and Treasury notes would be ________, ________ and ________ respectively if you decide to hold a complete portfolio that has an expected return of 8%.
A)$162, $595, $243
B)$243, $162, $595
C)$595, $162, $243
D)$595, $243, $162

Question

Quizplus · Accepted Answer

To achieve an expected return of 8%, the weights in the risky portfolio (P) and Treasury notes need to be calculated. The expected return of P is 0.6*14% + 0.4*10% = 12.4%. Let w be the weight in P, then 0.05*(1-w) + 0.124*w = 0.08. Solving gives w = 0.405. Therefore, $405 in P and $595 in Treasury notes. In P, $243 (60% of $405) in X and $162 (40% of $405) in Y.

You Are Considering Investing $1000 in a Complete Portfolio